Rockfish Historical Harvest Estimates

This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: rf_harvest_est_kha_rm_wt_thru2023_1500000_7kn_2025-05-29 (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.9962

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Model fit

Logbook residuals

Figure 18.- Residuals from logbook harvests.

SWHS residuals

Figure 19.- Residuals from SWHS harvests.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 21.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

## NULL

## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Weight Fits

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

### Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.

parameter n badRhat_avg beta0_pelagic 3 1.340126 beta1_pelagic 4 1.301010 beta1_pH 3 1.268308 tau_beta0_pelagic 1 1.250564 beta2_pelagic 4 1.245676 beta1_yellow 1 1.195736

parameter n badRhat_avg beta4_pelagic 1 1.183781 beta3_yellow 1 1.178719 beta2_pH 1 1.162528 tau_beta0_yellow 2 1.148813 beta1_black 1 1.140916 beta3_pelagic 2 1.140504

Table 2. Summary of unconverged parameters by area

	CI	CSEO	eastside	NSEI	NSEO	PWSI	PWSO	SOKO2SAP	SSEO	WKMA
beta0_pelagic	0	1	0	0	0	1	1	0	0	0
beta1_black	0	0	0	1	0	0	0	0	0	0
beta1_pelagic	0	1	0	0	0	1	1	0	1	0
beta1_pH	0	0	0	0	0	1	1	1	0	0
beta1_yellow	1	0	0	0	0	0	0	0	0	0
beta2_pelagic	0	1	0	1	0	1	1	0	0	0
beta2_pH	0	0	0	0	0	0	0	0	0	1
beta3_pelagic	0	1	0	0	0	0	1	0	0	0
beta3_yellow	0	0	0	0	1	0	0	0	0	0
beta4_pelagic	0	0	1	0	0	0	0	0	0	0
tau_beta0_pelagic	1	0	0	0	0	0	0	0	0	0
tau_beta0_yellow	1	0	0	0	0	1	0	0	0	0

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.132	0.071	-0.266	-0.134	0.019
mu_bc_H[2]	-0.099	0.043	-0.173	-0.102	-0.004
mu_bc_H[3]	-0.431	0.070	-0.566	-0.432	-0.285
mu_bc_H[4]	-0.989	0.195	-1.384	-0.989	-0.615
mu_bc_H[5]	0.952	0.994	-0.179	0.744	3.322
mu_bc_H[6]	-2.157	0.328	-2.789	-2.165	-1.472
mu_bc_H[7]	-0.462	0.106	-0.685	-0.458	-0.262
mu_bc_H[8]	0.248	0.362	-0.367	0.217	1.041
mu_bc_H[9]	-0.301	0.137	-0.565	-0.303	-0.032
mu_bc_H[10]	-0.108	0.070	-0.238	-0.111	0.039
mu_bc_H[11]	-0.124	0.038	-0.196	-0.124	-0.049
mu_bc_H[12]	-0.253	0.106	-0.483	-0.250	-0.053
mu_bc_H[13]	-0.132	0.079	-0.279	-0.134	0.029
mu_bc_H[14]	-0.301	0.097	-0.494	-0.298	-0.120
mu_bc_H[15]	-0.341	0.051	-0.434	-0.342	-0.233
mu_bc_H[16]	-0.260	0.385	-0.931	-0.286	0.618
mu_bc_R[1]	1.299	0.145	1.018	1.295	1.592
mu_bc_R[2]	1.453	0.096	1.255	1.456	1.638
mu_bc_R[3]	1.389	0.145	1.090	1.390	1.666
mu_bc_R[4]	0.919	0.204	0.484	0.924	1.281
mu_bc_R[5]	1.181	0.471	0.266	1.181	2.105
mu_bc_R[6]	-1.597	0.426	-2.437	-1.598	-0.771
mu_bc_R[7]	0.458	0.207	0.028	0.462	0.860
mu_bc_R[8]	0.551	0.197	0.154	0.553	0.916
mu_bc_R[9]	0.349	0.202	-0.097	0.362	0.708
mu_bc_R[10]	1.295	0.135	1.023	1.298	1.551
mu_bc_R[11]	1.042	0.096	0.852	1.041	1.226
mu_bc_R[12]	0.818	0.203	0.411	0.826	1.204
mu_bc_R[13]	1.028	0.103	0.825	1.029	1.224
mu_bc_R[14]	0.896	0.143	0.618	0.900	1.175
mu_bc_R[15]	0.779	0.109	0.569	0.780	0.989
mu_bc_R[16]	1.094	0.129	0.843	1.096	1.346
tau_pH[1]	5.133	0.459	4.265	5.125	6.030
tau_pH[2]	2.028	0.230	1.590	2.018	2.486
tau_pH[3]	2.138	0.217	1.736	2.133	2.594
beta0_pH[1,1]	0.553	0.175	0.197	0.560	0.877
beta0_pH[2,1]	1.389	0.199	1.038	1.387	1.732
beta0_pH[3,1]	1.434	0.190	1.025	1.441	1.776
beta0_pH[4,1]	1.570	0.217	1.117	1.585	1.955
beta0_pH[5,1]	-0.850	0.265	-1.440	-0.836	-0.378
beta0_pH[6,1]	-0.691	0.375	-1.566	-0.644	-0.080
beta0_pH[7,1]	-0.479	0.409	-1.357	-0.482	0.403
beta0_pH[8,1]	-0.650	0.275	-1.240	-0.620	-0.162
beta0_pH[9,1]	-0.637	0.277	-1.225	-0.618	-0.166
beta0_pH[10,1]	0.223	0.213	-0.204	0.230	0.626
beta0_pH[11,1]	-0.081	0.163	-0.408	-0.073	0.227
beta0_pH[12,1]	0.484	0.191	0.113	0.484	0.854
beta0_pH[13,1]	0.011	0.140	-0.260	0.010	0.284
beta0_pH[14,1]	-0.313	0.171	-0.662	-0.310	0.003
beta0_pH[15,1]	-0.032	0.171	-0.367	-0.033	0.305
beta0_pH[16,1]	-0.489	0.384	-1.412	-0.411	0.065
beta0_pH[1,2]	2.845	0.162	2.509	2.851	3.161
beta0_pH[2,2]	2.888	0.134	2.620	2.890	3.151
beta0_pH[3,2]	3.133	0.149	2.852	3.128	3.438
beta0_pH[4,2]	2.952	0.135	2.685	2.952	3.217
beta0_pH[5,2]	4.846	1.388	3.018	4.571	8.440
beta0_pH[6,2]	3.111	0.200	2.720	3.109	3.515
beta0_pH[7,2]	1.836	0.196	1.434	1.841	2.213
beta0_pH[8,2]	2.872	0.174	2.532	2.874	3.213
beta0_pH[9,2]	3.436	0.224	2.999	3.428	3.885
beta0_pH[10,2]	3.752	0.197	3.365	3.757	4.131
beta0_pH[11,2]	-4.851	0.304	-5.466	-4.846	-4.262
beta0_pH[12,2]	-4.781	0.399	-5.592	-4.766	-4.030
beta0_pH[13,2]	-4.568	0.391	-5.312	-4.576	-3.752
beta0_pH[14,2]	-5.609	0.453	-6.542	-5.596	-4.781
beta0_pH[15,2]	-4.273	0.350	-4.972	-4.275	-3.579
beta0_pH[16,2]	-4.861	0.383	-5.636	-4.858	-4.124
beta0_pH[1,3]	-0.162	0.712	-1.756	-0.066	0.990
beta0_pH[2,3]	2.188	0.161	1.873	2.189	2.496
beta0_pH[3,3]	2.528	0.150	2.230	2.526	2.830
beta0_pH[4,3]	2.966	0.162	2.643	2.969	3.288
beta0_pH[5,3]	2.131	1.391	0.398	1.838	5.650
beta0_pH[6,3]	1.005	0.502	-0.188	1.028	1.915
beta0_pH[7,3]	0.626	0.178	0.281	0.623	0.971
beta0_pH[8,3]	0.309	0.190	-0.067	0.304	0.676
beta0_pH[9,3]	-0.626	0.375	-1.562	-0.598	0.024
beta0_pH[10,3]	0.479	0.372	-0.456	0.526	1.083
beta0_pH[11,3]	-0.146	0.333	-0.764	-0.146	0.516
beta0_pH[12,3]	-0.854	0.351	-1.601	-0.830	-0.229
beta0_pH[13,3]	-0.142	0.305	-0.740	-0.143	0.454
beta0_pH[14,3]	-0.274	0.268	-0.798	-0.267	0.262
beta0_pH[15,3]	-0.689	0.292	-1.272	-0.687	-0.154
beta0_pH[16,3]	-0.396	0.293	-0.992	-0.392	0.170
beta1_pH[1,1]	3.077	0.318	2.515	3.055	3.754
beta1_pH[2,1]	2.131	0.324	1.629	2.119	2.723
beta1_pH[3,1]	1.960	0.301	1.425	1.942	2.627
beta1_pH[4,1]	2.377	0.333	1.822	2.344	3.128
beta1_pH[5,1]	2.285	0.319	1.729	2.260	3.020
beta1_pH[6,1]	3.736	0.958	2.351	3.566	6.034
beta1_pH[7,1]	2.584	0.792	1.062	2.580	4.307
beta1_pH[8,1]	3.842	0.881	2.568	3.677	6.058
beta1_pH[9,1]	2.314	0.357	1.709	2.288	3.092
beta1_pH[10,1]	2.413	0.288	1.873	2.398	3.023
beta1_pH[11,1]	3.255	0.206	2.851	3.252	3.665
beta1_pH[12,1]	2.553	0.225	2.119	2.552	2.984
beta1_pH[13,1]	2.961	0.205	2.568	2.955	3.385
beta1_pH[14,1]	3.416	0.222	2.991	3.413	3.864
beta1_pH[15,1]	2.535	0.218	2.112	2.534	2.977
beta1_pH[16,1]	4.123	0.677	3.174	3.999	5.788
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.000	0.015	0.000	0.000	0.001
beta1_pH[4,2]	0.000	0.002	0.000	0.000	0.001
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	6.689	0.332	6.035	6.689	7.347
beta1_pH[12,2]	6.440	0.459	5.562	6.426	7.375
beta1_pH[13,2]	6.948	0.432	6.106	6.951	7.786
beta1_pH[14,2]	7.248	0.478	6.375	7.237	8.193
beta1_pH[15,2]	6.750	0.384	5.993	6.740	7.506
beta1_pH[16,2]	7.452	0.425	6.648	7.450	8.307
beta1_pH[1,3]	4.693	1.680	2.114	4.402	8.297
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	4.065	7.187	0.864	2.806	15.793
beta1_pH[6,3]	4.134	12.658	0.381	2.616	11.194
beta1_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,3]	2.749	0.340	2.087	2.743	3.418
beta1_pH[9,3]	2.749	0.446	1.987	2.711	3.781
beta1_pH[10,3]	2.893	0.448	2.159	2.847	3.959
beta1_pH[11,3]	2.726	0.393	1.973	2.721	3.513
beta1_pH[12,3]	4.110	0.444	3.277	4.101	5.031
beta1_pH[13,3]	1.721	0.330	1.077	1.720	2.383
beta1_pH[14,3]	2.525	0.349	1.845	2.519	3.231
beta1_pH[15,3]	1.981	0.317	1.385	1.984	2.592
beta1_pH[16,3]	1.812	0.324	1.192	1.805	2.464
beta2_pH[1,1]	0.482	0.126	0.292	0.464	0.769
beta2_pH[2,1]	0.574	0.420	0.243	0.515	1.285
beta2_pH[3,1]	0.674	0.616	0.239	0.561	1.829
beta2_pH[4,1]	0.493	0.213	0.222	0.451	1.010
beta2_pH[5,1]	1.468	0.984	0.251	1.339	3.772
beta2_pH[6,1]	0.189	0.065	0.100	0.178	0.334
beta2_pH[7,1]	0.022	0.110	0.000	0.000	0.133
beta2_pH[8,1]	0.258	0.109	0.137	0.235	0.505
beta2_pH[9,1]	0.437	0.214	0.188	0.397	0.960
beta2_pH[10,1]	0.595	0.246	0.278	0.547	1.169
beta2_pH[11,1]	0.789	0.211	0.480	0.757	1.315
beta2_pH[12,1]	1.341	0.480	0.741	1.243	2.471
beta2_pH[13,1]	0.753	0.294	0.415	0.710	1.303
beta2_pH[14,1]	0.840	0.207	0.536	0.810	1.343
beta2_pH[15,1]	0.819	0.308	0.413	0.756	1.630
beta2_pH[16,1]	0.379	0.175	0.166	0.331	0.821
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	-2.222	1.973	-7.120	-1.711	-0.034
beta2_pH[4,2]	-2.033	1.860	-6.843	-1.540	-0.031
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	-9.455	4.297	-20.760	-8.482	-4.014
beta2_pH[12,2]	-7.973	4.997	-20.507	-7.156	-0.912
beta2_pH[13,2]	-7.755	4.970	-20.369	-6.711	-1.658
beta2_pH[14,2]	-8.445	4.625	-20.706	-7.456	-2.511
beta2_pH[15,2]	-9.268	4.369	-20.588	-8.251	-3.753
beta2_pH[16,2]	-9.417	4.266	-20.426	-8.467	-3.976
beta2_pH[1,3]	0.255	0.390	0.101	0.184	0.736
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	9.017	6.459	-0.296	8.072	24.080
beta2_pH[6,3]	9.223	6.313	0.211	8.174	24.206
beta2_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,3]	10.086	5.798	1.893	9.057	24.419
beta2_pH[9,3]	8.947	6.280	0.520	7.883	24.141
beta2_pH[10,3]	8.570	6.475	0.498	7.461	23.599
beta2_pH[11,3]	-2.278	2.144	-8.314	-1.681	-0.626
beta2_pH[12,3]	-2.408	1.991	-8.269	-1.828	-0.926
beta2_pH[13,3]	-2.877	2.377	-9.571	-2.182	-0.816
beta2_pH[14,3]	-2.750	2.215	-9.025	-2.089	-0.871
beta2_pH[15,3]	-2.939	2.257	-9.394	-2.205	-0.989
beta2_pH[16,3]	-2.903	2.336	-9.352	-2.181	-0.872
beta3_pH[1,1]	35.929	0.825	34.330	35.927	37.516
beta3_pH[2,1]	33.619	1.482	31.557	33.503	36.471
beta3_pH[3,1]	33.643	0.997	31.787	33.629	35.690
beta3_pH[4,1]	33.797	1.173	31.650	33.738	36.235
beta3_pH[5,1]	27.706	1.095	26.460	27.464	30.836
beta3_pH[6,1]	38.118	3.001	32.614	37.945	44.479
beta3_pH[7,1]	31.200	7.972	18.576	31.038	45.037
beta3_pH[8,1]	39.589	1.931	36.016	39.502	44.244
beta3_pH[9,1]	30.703	1.412	28.214	30.623	33.795
beta3_pH[10,1]	32.716	0.945	30.960	32.664	34.670
beta3_pH[11,1]	30.351	0.471	29.431	30.344	31.284
beta3_pH[12,1]	30.153	0.400	29.331	30.170	30.922
beta3_pH[13,1]	33.184	0.578	32.074	33.177	34.362
beta3_pH[14,1]	32.035	0.463	31.151	32.026	32.971
beta3_pH[15,1]	31.189	0.636	29.988	31.179	32.474
beta3_pH[16,1]	32.013	1.020	30.284	31.893	34.301
beta3_pH[1,2]	29.970	7.860	18.455	29.084	44.915
beta3_pH[2,2]	29.805	7.965	18.435	28.544	44.737
beta3_pH[3,2]	30.101	7.955	18.480	29.170	44.978
beta3_pH[4,2]	29.784	7.828	18.393	28.698	44.669
beta3_pH[5,2]	30.065	8.003	18.422	28.957	44.847
beta3_pH[6,2]	29.776	7.879	18.503	28.782	44.750
beta3_pH[7,2]	30.043	7.978	18.545	29.172	44.973
beta3_pH[8,2]	29.675	7.787	18.423	28.849	44.799
beta3_pH[9,2]	30.251	8.007	18.428	29.337	45.046
beta3_pH[10,2]	29.943	7.904	18.471	28.853	44.804
beta3_pH[11,2]	43.404	0.175	43.118	43.388	43.758
beta3_pH[12,2]	43.192	0.196	42.915	43.145	43.711
beta3_pH[13,2]	43.866	0.146	43.468	43.904	44.041
beta3_pH[14,2]	43.297	0.200	43.050	43.243	43.788
beta3_pH[15,2]	43.411	0.192	43.105	43.387	43.822
beta3_pH[16,2]	43.497	0.186	43.160	43.496	43.836
beta3_pH[1,3]	39.010	3.222	32.781	38.842	45.270
beta3_pH[2,3]	30.166	8.075	18.450	29.140	44.980
beta3_pH[3,3]	30.277	8.022	18.447	29.550	45.069
beta3_pH[4,3]	30.226	7.992	18.437	29.511	44.937
beta3_pH[5,3]	36.677	3.782	31.286	36.077	45.024
beta3_pH[6,3]	40.421	3.571	31.778	40.776	45.652
beta3_pH[7,3]	37.981	4.305	31.306	37.649	45.602
beta3_pH[8,3]	41.486	0.249	41.053	41.478	41.926
beta3_pH[9,3]	33.469	0.579	31.652	33.557	34.249
beta3_pH[10,3]	35.831	0.778	33.495	36.016	36.851
beta3_pH[11,3]	41.758	0.827	40.046	41.802	43.250
beta3_pH[12,3]	41.721	0.398	40.914	41.730	42.489
beta3_pH[13,3]	42.749	0.877	41.075	42.769	44.616
beta3_pH[14,3]	41.092	0.579	39.878	41.111	42.208
beta3_pH[15,3]	42.581	0.652	41.105	42.625	43.713
beta3_pH[16,3]	42.903	0.744	41.270	42.996	44.200
beta0_pelagic[1]	2.227	0.133	1.970	2.223	2.493
beta0_pelagic[2]	1.509	0.123	1.269	1.510	1.754
beta0_pelagic[3]	-0.852	0.919	-2.628	-0.768	0.521
beta0_pelagic[4]	-0.683	0.852	-2.376	-0.564	0.654
beta0_pelagic[5]	1.194	0.250	0.672	1.202	1.663
beta0_pelagic[6]	1.467	0.264	0.913	1.487	1.938
beta0_pelagic[7]	1.603	0.210	1.216	1.591	2.069
beta0_pelagic[8]	1.766	0.202	1.380	1.762	2.193
beta0_pelagic[9]	2.480	0.312	1.887	2.483	3.068
beta0_pelagic[10]	2.528	0.206	2.085	2.534	2.918
beta0_pelagic[11]	-0.057	0.489	-1.135	-0.012	0.691
beta0_pelagic[12]	1.677	0.149	1.368	1.679	1.964
beta0_pelagic[13]	0.270	0.245	-0.242	0.296	0.664
beta0_pelagic[14]	-0.153	0.298	-0.833	-0.120	0.334
beta0_pelagic[15]	-0.274	0.139	-0.555	-0.270	0.005
beta0_pelagic[16]	0.148	0.342	-0.611	0.213	0.652
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	2.769	1.567	0.539	2.647	5.831
beta1_pelagic[4]	2.337	1.329	0.604	1.957	5.622
beta1_pelagic[5]	-0.076	0.315	-0.698	-0.075	0.530
beta1_pelagic[6]	-0.098	0.445	-0.852	-0.157	0.732
beta1_pelagic[7]	-0.021	0.299	-0.639	-0.018	0.548
beta1_pelagic[8]	-0.010	0.275	-0.546	-0.016	0.532
beta1_pelagic[9]	0.208	0.491	-0.785	0.323	0.954
beta1_pelagic[10]	0.066	0.268	-0.450	0.062	0.621
beta1_pelagic[11]	4.080	1.122	2.287	4.063	6.187
beta1_pelagic[12]	2.810	0.350	2.200	2.793	3.506
beta1_pelagic[13]	3.183	0.881	1.790	3.080	5.039
beta1_pelagic[14]	4.589	0.996	2.965	4.477	6.772
beta1_pelagic[15]	2.947	0.278	2.381	2.956	3.461
beta1_pelagic[16]	4.141	1.169	2.719	3.744	6.778
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	0.408	1.592	0.026	0.091	3.108
beta2_pelagic[4]	0.732	2.027	0.021	0.256	5.555
beta2_pelagic[5]	0.014	0.665	-1.387	0.000	1.480
beta2_pelagic[6]	-0.106	0.648	-1.451	-0.125	1.175
beta2_pelagic[7]	0.003	0.631	-1.347	0.003	1.379
beta2_pelagic[8]	0.016	0.617	-1.263	0.003	1.315
beta2_pelagic[9]	0.180	0.666	-1.288	0.244	1.478
beta2_pelagic[10]	0.013	0.555	-1.172	0.016	1.203
beta2_pelagic[11]	1.377	3.821	0.105	0.220	14.672
beta2_pelagic[12]	5.468	4.792	0.922	3.989	18.715
beta2_pelagic[13]	0.892	2.265	0.160	0.391	5.690
beta2_pelagic[14]	0.296	0.140	0.151	0.271	0.603
beta2_pelagic[15]	5.718	4.538	1.090	4.451	16.910
beta2_pelagic[16]	3.272	5.002	0.171	0.547	17.578
beta3_pelagic[1]	29.783	7.807	18.424	28.882	44.768
beta3_pelagic[2]	30.078	7.857	18.506	29.159	44.923
beta3_pelagic[3]	29.138	7.085	18.651	28.423	44.701
beta3_pelagic[4]	24.917	5.551	18.389	23.673	40.753
beta3_pelagic[5]	29.956	8.177	18.477	28.545	45.298
beta3_pelagic[6]	31.806	6.772	19.132	31.797	44.007
beta3_pelagic[7]	30.024	7.971	18.358	29.041	45.047
beta3_pelagic[8]	29.677	7.970	18.410	28.508	44.846
beta3_pelagic[9]	30.888	5.995	19.191	31.041	42.967
beta3_pelagic[10]	29.648	8.170	18.366	28.470	45.025
beta3_pelagic[11]	42.504	2.173	36.580	43.068	45.491
beta3_pelagic[12]	43.477	0.304	42.969	43.463	44.004
beta3_pelagic[13]	43.098	1.479	40.347	43.038	45.755
beta3_pelagic[14]	42.570	1.610	39.216	42.589	45.599
beta3_pelagic[15]	43.167	0.272	42.522	43.179	43.679
beta3_pelagic[16]	43.124	1.124	40.349	43.211	45.424
mu_beta0_pelagic[1]	0.495	1.168	-1.944	0.576	2.829
mu_beta0_pelagic[2]	1.815	0.395	1.029	1.820	2.599
mu_beta0_pelagic[3]	0.269	0.479	-0.693	0.265	1.246
tau_beta0_pelagic[1]	0.376	0.448	0.046	0.224	1.656
tau_beta0_pelagic[2]	2.727	2.873	0.232	1.985	9.406
tau_beta0_pelagic[3]	1.448	1.136	0.165	1.154	4.393
beta0_yellow[1]	-0.541	0.189	-0.967	-0.525	-0.233
beta0_yellow[2]	0.492	0.187	0.119	0.507	0.797
beta0_yellow[3]	-0.327	0.204	-0.752	-0.315	0.009
beta0_yellow[4]	0.858	0.259	0.200	0.900	1.221
beta0_yellow[5]	-0.280	0.356	-0.995	-0.286	0.405
beta0_yellow[6]	1.116	0.168	0.788	1.114	1.457
beta0_yellow[7]	0.982	0.159	0.665	0.982	1.291
beta0_yellow[8]	1.011	0.152	0.717	1.015	1.307
beta0_yellow[9]	0.664	0.158	0.355	0.665	0.977
beta0_yellow[10]	0.574	0.142	0.297	0.574	0.860
beta0_yellow[11]	-2.028	0.427	-2.908	-2.010	-1.224
beta0_yellow[12]	-3.705	0.419	-4.588	-3.687	-2.943
beta0_yellow[13]	-3.734	0.496	-4.824	-3.679	-2.893
beta0_yellow[14]	-2.161	0.522	-3.109	-2.191	-0.983
beta0_yellow[15]	-2.861	0.409	-3.681	-2.846	-2.114
beta0_yellow[16]	-2.425	0.450	-3.302	-2.427	-1.545
beta1_yellow[1]	0.835	1.625	0.008	0.648	2.537
beta1_yellow[2]	1.067	0.408	0.572	1.010	2.038
beta1_yellow[3]	0.717	0.296	0.229	0.701	1.314
beta1_yellow[4]	1.315	0.713	0.629	1.141	3.564
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	2.171	0.428	1.351	2.153	3.035
beta1_yellow[12]	2.496	0.431	1.705	2.469	3.416
beta1_yellow[13]	2.856	0.495	2.028	2.802	3.956
beta1_yellow[14]	2.244	0.502	1.191	2.259	3.231
beta1_yellow[15]	2.114	0.405	1.357	2.109	2.935
beta1_yellow[16]	2.183	0.446	1.299	2.194	3.074
beta2_yellow[1]	-3.920	3.221	-11.657	-3.143	-0.049
beta2_yellow[2]	-4.110	3.214	-11.753	-3.295	-0.161
beta2_yellow[3]	-3.852	3.205	-11.656	-3.118	-0.150
beta2_yellow[4]	-3.501	3.318	-11.609	-2.551	-0.112
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	-4.721	2.867	-12.389	-4.075	-1.092
beta2_yellow[12]	-5.088	2.875	-12.588	-4.433	-1.381
beta2_yellow[13]	-4.868	2.685	-11.831	-4.200	-1.515
beta2_yellow[14]	-4.936	3.070	-12.744	-4.296	-0.510
beta2_yellow[15]	-4.495	2.856	-12.043	-3.814	-1.018
beta2_yellow[16]	-5.036	2.902	-12.574	-4.402	-1.271
beta3_yellow[1]	25.913	7.138	18.270	22.861	44.245
beta3_yellow[2]	29.185	1.946	25.622	28.909	33.183
beta3_yellow[3]	32.894	3.257	24.787	32.801	40.317
beta3_yellow[4]	29.023	3.478	21.865	27.988	36.208
beta3_yellow[5]	29.734	7.932	18.418	28.495	45.038
beta3_yellow[6]	30.225	7.969	18.451	29.447	45.055
beta3_yellow[7]	30.183	7.905	18.585	29.494	44.862
beta3_yellow[8]	30.152	8.087	18.411	29.155	45.011
beta3_yellow[9]	30.294	7.974	18.511	29.476	44.983
beta3_yellow[10]	29.822	7.861	18.538	28.862	44.709
beta3_yellow[11]	45.368	0.483	44.241	45.462	45.974
beta3_yellow[12]	43.303	0.393	42.548	43.283	44.059
beta3_yellow[13]	44.876	0.385	43.993	44.949	45.528
beta3_yellow[14]	44.105	1.527	41.733	44.247	45.803
beta3_yellow[15]	45.173	0.521	44.169	45.147	45.971
beta3_yellow[16]	44.551	0.689	43.363	44.533	45.850
mu_beta0_yellow[1]	0.111	0.564	-1.073	0.106	1.262
mu_beta0_yellow[2]	0.649	0.334	-0.059	0.673	1.270
mu_beta0_yellow[3]	-2.497	0.622	-3.508	-2.567	-1.013
tau_beta0_yellow[1]	1.815	2.927	0.099	1.130	6.987
tau_beta0_yellow[2]	3.676	4.126	0.326	2.437	14.493
tau_beta0_yellow[3]	1.548	2.620	0.105	0.988	5.959
beta0_black[1]	-0.076	0.161	-0.394	-0.078	0.238
beta0_black[2]	1.917	0.133	1.654	1.916	2.172
beta0_black[3]	1.314	0.134	1.047	1.313	1.571
beta0_black[4]	2.433	0.131	2.182	2.431	2.686
beta0_black[5]	4.612	2.084	1.819	4.198	9.960
beta0_black[6]	4.584	1.854	2.281	4.114	9.512
beta0_black[7]	3.744	1.927	1.572	3.260	8.991
beta0_black[8]	0.948	0.215	0.543	0.940	1.402
beta0_black[9]	2.607	0.232	2.163	2.603	3.077
beta0_black[10]	1.460	0.135	1.191	1.458	1.720
beta0_black[11]	3.486	0.155	3.178	3.484	3.785
beta0_black[12]	4.863	0.179	4.513	4.870	5.201
beta0_black[13]	-0.142	0.268	-0.694	-0.119	0.307
beta0_black[14]	2.855	0.160	2.537	2.855	3.158
beta0_black[15]	1.292	0.156	0.992	1.294	1.613
beta0_black[16]	4.275	0.159	3.969	4.276	4.581
beta2_black[1]	7.367	9.562	0.536	3.306	38.399
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-1.784	1.538	-6.141	-1.301	-0.287
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	41.764	1.178	39.961	41.916	43.365
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	39.080	1.306	36.579	39.269	40.570
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.260	0.198	-0.645	-0.262	0.138
beta4_black[2]	0.240	0.190	-0.128	0.238	0.615
beta4_black[3]	-0.931	0.195	-1.314	-0.931	-0.554
beta4_black[4]	0.421	0.213	-0.009	0.423	0.851
beta4_black[5]	0.531	1.234	-1.342	0.320	3.646
beta4_black[6]	0.539	1.235	-1.270	0.331	3.598
beta4_black[7]	0.486	1.269	-1.319	0.277	3.858
beta4_black[8]	-0.239	0.320	-0.884	-0.233	0.367
beta4_black[9]	0.833	0.795	-0.252	0.665	2.873
beta4_black[10]	0.047	0.186	-0.326	0.049	0.417
beta4_black[11]	-0.696	0.216	-1.113	-0.694	-0.271
beta4_black[12]	0.172	0.320	-0.429	0.169	0.805
beta4_black[13]	-1.185	0.222	-1.629	-1.183	-0.751
beta4_black[14]	-0.177	0.239	-0.628	-0.186	0.316
beta4_black[15]	-0.885	0.217	-1.297	-0.889	-0.468
beta4_black[16]	-0.601	0.232	-1.058	-0.596	-0.164
mu_beta0_black[1]	1.278	0.934	-0.806	1.304	3.097
mu_beta0_black[2]	2.727	1.057	0.858	2.627	5.160
mu_beta0_black[3]	2.505	0.984	0.384	2.552	4.345
tau_beta0_black[1]	0.625	0.600	0.057	0.438	2.199
tau_beta0_black[2]	0.436	0.620	0.045	0.248	1.906
tau_beta0_black[3]	0.239	0.162	0.051	0.201	0.661
beta0_dsr[11]	-2.893	0.295	-3.464	-2.902	-2.320
beta0_dsr[12]	4.556	0.309	3.999	4.555	5.137
beta0_dsr[13]	-1.340	0.293	-1.930	-1.335	-0.769
beta0_dsr[14]	-3.664	0.517	-4.681	-3.657	-2.637
beta0_dsr[15]	-1.934	0.284	-2.492	-1.937	-1.387
beta0_dsr[16]	-3.002	0.371	-3.741	-2.998	-2.272
beta1_dsr[11]	4.825	0.307	4.234	4.829	5.423
beta1_dsr[12]	6.461	6.522	2.305	5.059	19.555
beta1_dsr[13]	2.847	0.309	2.261	2.836	3.434
beta1_dsr[14]	6.333	0.542	5.263	6.326	7.416
beta1_dsr[15]	3.333	0.285	2.780	3.336	3.884
beta1_dsr[16]	5.818	0.393	5.067	5.813	6.593
beta2_dsr[11]	-8.120	2.165	-12.988	-7.833	-4.632
beta2_dsr[12]	-7.014	2.651	-13.089	-6.840	-2.241
beta2_dsr[13]	-6.543	2.657	-12.332	-6.422	-1.771
beta2_dsr[14]	-6.192	2.719	-12.156	-6.035	-1.776
beta2_dsr[15]	-7.733	2.406	-13.304	-7.417	-3.785
beta2_dsr[16]	-7.887	2.361	-13.518	-7.572	-4.238
beta3_dsr[11]	43.486	0.150	43.217	43.476	43.780
beta3_dsr[12]	33.969	0.741	32.140	34.122	34.830
beta3_dsr[13]	43.246	0.281	42.797	43.193	43.854
beta3_dsr[14]	43.344	0.224	43.072	43.281	43.914
beta3_dsr[15]	43.507	0.189	43.165	43.511	43.850
beta3_dsr[16]	43.437	0.156	43.172	43.422	43.761
beta4_dsr[11]	0.588	0.219	0.159	0.590	1.027
beta4_dsr[12]	0.254	0.437	-0.626	0.262	1.103
beta4_dsr[13]	-0.161	0.222	-0.604	-0.161	0.270
beta4_dsr[14]	0.157	0.251	-0.339	0.164	0.652
beta4_dsr[15]	0.724	0.219	0.305	0.721	1.179
beta4_dsr[16]	0.150	0.226	-0.289	0.150	0.585
beta0_slope[11]	-1.846	0.148	-2.144	-1.847	-1.556
beta0_slope[12]	-4.471	0.262	-4.990	-4.464	-3.969
beta0_slope[13]	-1.352	0.190	-1.788	-1.337	-1.023
beta0_slope[14]	-2.674	0.167	-3.005	-2.671	-2.350
beta0_slope[15]	-1.341	0.146	-1.635	-1.340	-1.059
beta0_slope[16]	-2.738	0.157	-3.040	-2.743	-2.422
beta1_slope[11]	4.484	0.218	4.062	4.482	4.916
beta1_slope[12]	3.985	0.441	3.138	3.991	4.855
beta1_slope[13]	2.731	0.463	2.202	2.655	4.279
beta1_slope[14]	6.319	0.425	5.493	6.314	7.162
beta1_slope[15]	3.007	0.211	2.588	3.007	3.421
beta1_slope[16]	5.286	0.294	4.710	5.279	5.876
beta2_slope[11]	8.687	2.369	5.158	8.330	14.505
beta2_slope[12]	6.624	2.925	1.219	6.684	12.701
beta2_slope[13]	5.330	3.104	0.352	5.306	11.521
beta2_slope[14]	6.393	2.604	2.334	6.143	12.150
beta2_slope[15]	8.237	2.384	4.430	7.932	13.758
beta2_slope[16]	7.769	2.295	4.237	7.435	13.337
beta3_slope[11]	43.463	0.134	43.224	43.458	43.722
beta3_slope[12]	43.351	0.279	42.860	43.319	43.907
beta3_slope[13]	43.456	0.411	42.862	43.399	44.062
beta3_slope[14]	43.269	0.137	43.093	43.236	43.620
beta3_slope[15]	43.491	0.164	43.193	43.489	43.802
beta3_slope[16]	43.374	0.141	43.156	43.353	43.685
beta4_slope[11]	-0.729	0.164	-1.045	-0.732	-0.406
beta4_slope[12]	-1.167	0.457	-2.164	-1.131	-0.380
beta4_slope[13]	0.092	0.162	-0.217	0.091	0.411
beta4_slope[14]	-0.090	0.193	-0.463	-0.093	0.282
beta4_slope[15]	-0.766	0.162	-1.081	-0.765	-0.444
beta4_slope[16]	-0.159	0.175	-0.494	-0.157	0.178
sigma_H[1]	0.199	0.054	0.103	0.196	0.318
sigma_H[2]	0.172	0.030	0.118	0.169	0.238
sigma_H[3]	0.196	0.042	0.121	0.193	0.288
sigma_H[4]	0.419	0.075	0.295	0.411	0.588
sigma_H[5]	0.998	0.207	0.614	0.989	1.413
sigma_H[6]	0.389	0.210	0.025	0.382	0.842
sigma_H[7]	0.309	0.064	0.210	0.301	0.462
sigma_H[8]	0.416	0.093	0.266	0.408	0.615
sigma_H[9]	0.523	0.126	0.327	0.509	0.808
sigma_H[10]	0.215	0.043	0.139	0.211	0.311
sigma_H[11]	0.278	0.045	0.201	0.274	0.376
sigma_H[12]	0.437	0.165	0.206	0.419	0.774
sigma_H[13]	0.215	0.038	0.150	0.211	0.300
sigma_H[14]	0.509	0.095	0.342	0.503	0.724
sigma_H[15]	0.246	0.041	0.178	0.242	0.337
sigma_H[16]	0.227	0.044	0.155	0.222	0.326
lambda_H[1]	3.228	4.339	0.158	1.825	14.593
lambda_H[2]	8.364	7.285	0.883	6.234	27.764
lambda_H[3]	6.117	9.311	0.240	3.076	31.943
lambda_H[4]	0.006	0.004	0.001	0.005	0.018
lambda_H[5]	3.748	8.211	0.040	1.044	28.106
lambda_H[6]	7.471	15.021	0.008	0.882	48.366
lambda_H[7]	0.013	0.009	0.002	0.011	0.035
lambda_H[8]	8.341	10.706	0.114	4.730	38.056
lambda_H[9]	0.015	0.010	0.003	0.013	0.040
lambda_H[10]	0.313	0.571	0.032	0.196	1.159
lambda_H[11]	0.272	0.408	0.012	0.132	1.210
lambda_H[12]	4.800	6.267	0.155	2.716	22.206
lambda_H[13]	3.549	3.273	0.222	2.705	11.992
lambda_H[14]	3.512	4.480	0.218	2.120	15.331
lambda_H[15]	0.026	0.038	0.003	0.017	0.112
lambda_H[16]	0.856	1.234	0.042	0.422	4.259
mu_lambda_H[1]	4.376	1.890	1.317	4.162	8.537
mu_lambda_H[2]	3.824	1.924	0.665	3.654	7.856
mu_lambda_H[3]	3.569	1.885	0.762	3.300	7.826
sigma_lambda_H[1]	8.581	4.230	2.249	7.905	18.329
sigma_lambda_H[2]	8.374	4.651	1.222	7.737	18.394
sigma_lambda_H[3]	6.367	3.982	0.981	5.520	16.021
beta_H[1,1]	6.913	1.087	4.277	7.100	8.525
beta_H[2,1]	9.885	0.481	8.826	9.914	10.770
beta_H[3,1]	7.975	0.788	6.101	8.081	9.227
beta_H[4,1]	9.423	7.839	-6.854	9.672	24.283
beta_H[5,1]	0.078	2.256	-4.607	0.178	3.915
beta_H[6,1]	3.021	4.114	-6.996	4.536	7.576
beta_H[7,1]	0.514	5.731	-11.570	0.903	10.706
beta_H[8,1]	1.383	3.911	-2.300	1.223	3.580
beta_H[9,1]	13.090	5.736	2.243	13.088	24.747
beta_H[10,1]	7.026	1.717	3.420	7.083	10.210
beta_H[11,1]	5.131	3.481	-2.751	5.894	9.936
beta_H[12,1]	2.591	1.089	0.715	2.525	4.912
beta_H[13,1]	9.025	0.930	6.921	9.106	10.535
beta_H[14,1]	2.203	1.070	0.143	2.180	4.407
beta_H[15,1]	-6.015	3.866	-13.028	-6.233	2.480
beta_H[16,1]	3.462	2.622	-0.729	3.176	9.876
beta_H[1,2]	7.910	0.238	7.434	7.915	8.364
beta_H[2,2]	10.029	0.132	9.774	10.031	10.284
beta_H[3,2]	8.952	0.197	8.574	8.950	9.363
beta_H[4,2]	3.540	1.513	0.790	3.495	6.778
beta_H[5,2]	1.929	0.930	0.092	1.951	3.718
beta_H[6,2]	5.724	1.050	3.254	5.877	7.368
beta_H[7,2]	2.678	1.074	0.752	2.614	4.972
beta_H[8,2]	3.000	1.084	1.310	3.138	4.203
beta_H[9,2]	3.495	1.132	1.234	3.458	5.838
beta_H[10,2]	8.210	0.348	7.494	8.221	8.863
beta_H[11,2]	9.770	0.639	8.822	9.654	11.197
beta_H[12,2]	3.937	0.374	3.242	3.924	4.719
beta_H[13,2]	9.123	0.255	8.661	9.111	9.622
beta_H[14,2]	4.023	0.353	3.346	4.016	4.738
beta_H[15,2]	11.347	0.685	9.866	11.397	12.606
beta_H[16,2]	4.553	0.831	2.985	4.557	6.235
beta_H[1,3]	8.470	0.246	8.022	8.456	8.984
beta_H[2,3]	10.069	0.115	9.847	10.068	10.313
beta_H[3,3]	9.616	0.168	9.288	9.611	9.964
beta_H[4,3]	-2.502	0.883	-4.235	-2.495	-0.847
beta_H[5,3]	3.829	0.604	2.608	3.841	4.974
beta_H[6,3]	8.030	1.210	6.355	7.668	10.623
beta_H[7,3]	-2.785	0.661	-4.131	-2.768	-1.540
beta_H[8,3]	5.251	0.494	4.657	5.185	6.235
beta_H[9,3]	-2.840	0.729	-4.337	-2.809	-1.468
beta_H[10,3]	8.685	0.285	8.131	8.677	9.257
beta_H[11,3]	8.545	0.284	7.917	8.567	9.034
beta_H[12,3]	5.244	0.324	4.496	5.286	5.763
beta_H[13,3]	8.841	0.176	8.483	8.844	9.170
beta_H[14,3]	5.723	0.271	5.151	5.739	6.208
beta_H[15,3]	10.366	0.309	9.781	10.366	10.979
beta_H[16,3]	6.266	0.604	4.922	6.329	7.283
beta_H[1,4]	8.265	0.180	7.874	8.279	8.574
beta_H[2,4]	10.134	0.117	9.885	10.140	10.345
beta_H[3,4]	10.113	0.165	9.749	10.130	10.392
beta_H[4,4]	11.790	0.449	10.862	11.795	12.654
beta_H[5,4]	5.461	0.728	4.247	5.393	7.132
beta_H[6,4]	7.051	0.935	4.984	7.334	8.332
beta_H[7,4]	8.276	0.353	7.537	8.278	8.938
beta_H[8,4]	6.714	0.254	6.255	6.724	7.153
beta_H[9,4]	7.212	0.468	6.326	7.204	8.175
beta_H[10,4]	7.758	0.238	7.314	7.749	8.256
beta_H[11,4]	9.386	0.203	9.002	9.386	9.792
beta_H[12,4]	7.148	0.214	6.738	7.141	7.606
beta_H[13,4]	9.044	0.139	8.757	9.046	9.312
beta_H[14,4]	7.726	0.214	7.308	7.726	8.145
beta_H[15,4]	9.464	0.230	9.005	9.465	9.913
beta_H[16,4]	9.339	0.240	8.917	9.326	9.843
beta_H[1,5]	8.991	0.142	8.709	8.993	9.276
beta_H[2,5]	10.785	0.092	10.612	10.785	10.972
beta_H[3,5]	10.921	0.173	10.618	10.910	11.285
beta_H[4,5]	8.388	0.462	7.488	8.373	9.306
beta_H[5,5]	5.437	0.570	4.124	5.478	6.480
beta_H[6,5]	8.789	0.634	7.875	8.637	10.281
beta_H[7,5]	6.758	0.337	6.120	6.744	7.437
beta_H[8,5]	8.221	0.216	7.867	8.204	8.655
beta_H[9,5]	8.219	0.489	7.247	8.227	9.181
beta_H[10,5]	10.094	0.231	9.612	10.096	10.538
beta_H[11,5]	11.506	0.230	11.053	11.505	11.955
beta_H[12,5]	8.480	0.201	8.084	8.479	8.883
beta_H[13,5]	10.006	0.131	9.744	10.005	10.263
beta_H[14,5]	9.190	0.229	8.768	9.183	9.670
beta_H[15,5]	11.172	0.243	10.693	11.176	11.631
beta_H[16,5]	9.919	0.181	9.565	9.922	10.278
beta_H[1,6]	10.171	0.183	9.838	10.155	10.559
beta_H[2,6]	11.512	0.106	11.298	11.513	11.721
beta_H[3,6]	10.811	0.163	10.447	10.822	11.104
beta_H[4,6]	12.870	0.835	11.193	12.900	14.513
beta_H[5,6]	5.882	0.602	4.752	5.871	7.093
beta_H[6,6]	8.754	0.668	6.974	8.877	9.726
beta_H[7,6]	9.873	0.567	8.699	9.888	10.976
beta_H[8,6]	9.508	0.289	8.988	9.522	9.967
beta_H[9,6]	8.455	0.805	6.895	8.447	10.101
beta_H[10,6]	9.511	0.312	8.840	9.529	10.075
beta_H[11,6]	10.813	0.334	10.108	10.826	11.423
beta_H[12,6]	9.376	0.256	8.886	9.372	9.891
beta_H[13,6]	11.045	0.167	10.752	11.035	11.387
beta_H[14,6]	9.833	0.291	9.240	9.834	10.397
beta_H[15,6]	10.836	0.427	9.983	10.831	11.691
beta_H[16,6]	10.527	0.243	9.991	10.539	10.971
beta_H[1,7]	10.896	0.815	8.887	10.994	12.252
beta_H[2,7]	12.215	0.433	11.330	12.220	13.082
beta_H[3,7]	10.560	0.672	9.110	10.608	11.698
beta_H[4,7]	2.487	4.234	-6.002	2.404	11.003
beta_H[5,7]	6.422	1.817	3.090	6.373	10.337
beta_H[6,7]	9.623	2.344	5.131	9.493	15.711
beta_H[7,7]	10.459	2.884	4.727	10.383	16.231
beta_H[8,7]	10.965	1.103	9.429	10.911	12.637
beta_H[9,7]	4.586	4.105	-4.056	4.712	12.486
beta_H[10,7]	9.827	1.456	7.115	9.777	13.046
beta_H[11,7]	10.949	1.628	7.841	10.901	14.333
beta_H[12,7]	9.999	0.975	7.873	10.076	11.648
beta_H[13,7]	11.669	0.782	9.958	11.762	12.913
beta_H[14,7]	10.408	0.956	8.226	10.471	12.082
beta_H[15,7]	12.009	2.254	7.586	11.976	16.617
beta_H[16,7]	12.303	1.330	10.152	12.094	15.440
beta0_H[1]	8.617	13.395	-19.343	8.433	36.131
beta0_H[2]	10.659	6.117	-2.644	10.868	22.737
beta0_H[3]	10.292	10.261	-9.244	10.080	32.230
beta0_H[4]	5.982	182.137	-358.836	4.450	386.424
beta0_H[5]	4.033	23.806	-41.871	3.994	52.179
beta0_H[6]	6.852	49.689	-101.652	7.496	117.032
beta0_H[7]	8.483	135.531	-258.679	9.302	283.314
beta0_H[8]	6.008	36.415	-16.130	6.522	28.795
beta0_H[9]	4.446	116.441	-220.362	3.548	243.677
beta0_H[10]	7.612	33.331	-61.274	7.792	73.290
beta0_H[11]	9.105	49.520	-89.617	8.922	110.418
beta0_H[12]	6.855	12.128	-15.629	6.744	30.354
beta0_H[13]	9.890	10.972	-10.105	9.838	30.869
beta0_H[14]	6.666	11.097	-16.605	7.052	28.032
beta0_H[15]	7.908	111.206	-221.715	8.337	231.189
beta0_H[16]	8.158	26.894	-48.459	8.117	62.889